# What is the standard form of  y=(x - 8) (x + 10) (x - 40) (x + 8) ?

Jan 3, 2016

$y = {x}^{4} - 30 {x}^{3} - 464 {x}^{2} + 1920 x + 25600$

#### Explanation:

$y = \left(x - 8\right) \left(x + 10\right) \left(x - 40\right) \left(x + 8\right)$

$= \left(x - 8\right) \left(x + 8\right) \left(x + 10\right) \left(x - 40\right)$

$= \left({x}^{2} - 64\right) \left({x}^{2} - 30 x - 400\right)$

$= {x}^{2} \left({x}^{2} - 30 x - 400\right) - 64 \left({x}^{2} - 30 x - 400\right)$

$= {x}^{4} - 30 {x}^{3} - 400 {x}^{2} - 64 {x}^{2} + 1920 x + 25600$

$= {x}^{4} - 30 {x}^{3} - 464 {x}^{2} + 1920 x + 25600$

Standard form arranges the powers of $x$ (or whatever the variable is) in descending order.